Hybrid variation-perturbation method for calculating rovibrational energy levels of polyatomic molecules

A procedure for calculation of rotation-vibration states of medium sized molecules is presented. It combines the advantages of variational calculations and perturbation theory. The vibrational problem is solved by diagonalizing a Hamiltonian matrix, which is partitioned into two sub-blocks. The first, smaller sub-block includes matrix elements with the largest contribution to the energy levels targeted in the calculations. The second, larger sub-block comprises those basis states which have little effect on these energy levels. Numerical perturbation theory, implemented as a Jacobi rotation, is used to compute the contributions from the matrix elements of the second sub-block. Only the first sub-block needs to be stored in memory and diagonalized. Calculations of the vibrational-rotational energy levels also employ a partitioning of the Hamiltonian matrix into sub-blocks, each of which corresponds either to a single vibrational state or a set of resonating vibrational states, with all associated rotational levels. Physically, this partitioning is efficient when the Coriolis coupling between different vibrational states is small. Numerical perturbation theory is used to include the cross-contributions from different vibrational states. Separate individual sub-blocks are then diagonalized, replacing the diagonalization of a large Hamiltonian matrix with a number of small matrix diagonalizations. Numerical examples show that the proposed hybrid variational-perturbation method greatly speeds up the variational procedure without significant loss of precision for both vibrational-rotational energy levels and transition intensities. The hybrid scheme can be used for accurate nuclear motion calculations on molecules with up to 15 atoms on currently available computers.Comment: Molecular Physics (Handy Special Issue), in pres

MARVEL analysis of the measured high-resolution rovibronic spectra of the calcium monohydroxide radical (CaOH)

The calcium monohydroxide radical (CaOH) is an important astrophysical molecule relevant to cool stars and rocky exoplanets, amongst other astronomical environments. Here, we present a consistent set of highly accurate rovibronic (rotation-vibration-electronic) energy levels for the five lowest electronic states (\tilde{X}\,^2\Sigma^+, \tilde{A}\,^2\Pi, \tilde{B}\,^2\Sigma^+, \tilde{C}\,^2\Delta, \tilde{D}\,^2\Sigma^+) of CaOH. A comprehensive analysis of the published spectroscopic literature on this system has allowed 1955 energy levels to be determined from 3204 rovibronic experimental transitions, all with unique quantum number labelling and measurement uncertainties. The dataset covers rotational excitation up to $J=62.5$ for molecular states below 29\,000~cm$^{-1}$. The analysis was performed using the MARVEL algorithm, which is a robust procedure based on the theory of spectroscopic networks. The dataset provided will significantly aid future interstellar, circumstellar and atmospheric detections of CaOH, as well as assisting in the design of efficient laser cooling schemes in ultracold molecule research and precision tests of fundamental physics

The role of non-gray model atmospheres in the evolution of low mass metal poor stars

Gray model atmospheres are generally considered a reasonable approximation to make upon stars of mass greater than about 0.6 M-circle dot. Here we show that non-gray atmospheres can significantly affect evolutionary models, with masses up to 0.9 M-circle dot. The effect of including a non-gray atmosphere is strongest in the pre-main and post-main Sequence. This may have implications for the ages of the oldest globular clusters

A potential new method for determining the temperature of cool stars

‘The definitive version is available at www.blackwell-synergy.com.’ Copyright Blackwell Publishing DOI: 10.1111/j.1365-2966.2008.13489.xPeer reviewe

Beyond the Born-Oppenheimer approximation: high-resolution overtone spectroscopy of H2D+ and D2H+

Transitions to overtone 2v2 and 2v3, and combination v2 + v3 vibrations in jet-cooled H2D+ and D2H+ molecular ions have been measured for the first time by high-resolution IR spectroscopy. The source of these ions is a pulsed slit jet supersonic discharge, which allows for efficient generation, rotational cooling, and high frequency (100 KHz) concentration modulation for detection via sensitive lock-in detection methods. Isotopic substitution and high-resolution overtone spectroscopy in this fundamental molecular ion permit a systematic, first principles investigation of Born–Oppenheimer "breakdown" effects due to large amplitude vibrational motion as well as provide rigorous tests of approximate theoretical methods beyond the Born–Oppenheimer level. The observed overtone transitions are in remarkably good agreement (<0.1 cm–1) with non-Born–Oppenheimer ab initio theoretical predictions, with small but systematic deviations for 2v2, 2v + 3v, and 2v3 excited states indicating directions for further improvement in such treatments. Spectroscopic assignment and analysis of the isotopomeric transitions reveals strong Coriolis mixing between near resonant 2v3 and 2v + 3v vibrations in D2H+. Population-independent line intensity ratios for transitions from common lower states indicate excellent overall agreement with theoretical predictions for D2H+, but with statistically significant discrepancies noted for H2D+. Finally, H2D+ versus D2H+ isotopomer populations are analyzed as a function of D2/H2 mixing ratio and can be well described by steady state kinetics in the slit discharge expansion

A near infrared line list for \NH: Analysis of a Kitt Peak spectrum after 35 years

A Fourier Transform (FT) absorption spectrum of room temperature NH3 in the region 7400 - 8600 cm-1 is analysed using a variational line list and ground state energies determined using the MARVEL procedure. The spectrum was measured by Dr Catherine de Bergh in 1980 and is available from the Kitt Peak data center. The centers and intensities of 8468 ammonia lines were retrieved using a multiline fitting procedure. 2474 lines are assigned to 21 bands providing 1692 experimental energies in the range 7000 - 9000 cm-1. The spectrum was assigned by the joint use of the BYTe variational line list and combination differences. The assignments and experimental energies presented in this work are the first for ammonia in the region 7400 - 8600 cm-1, considerably extending the range of known vibrational-excited statesComment: 27 pages, 6 table, 5 figures. Accepted for publication in Journal of Molecular Spectroscop

Low temperature scattering with the R-matrix method: the Morse potential

Experiments are starting to probe collisions and chemical reactions between atoms and molecules at ultra-low temperatures. We have developed a new theoretical procedure for studying these collisions using the R-matrix method. Here this method is tested for the atom -- atom collisions described by a Morse potential. Analytic solutions for continuum states of the Morse potential are derived and compared with numerical results computed using an R-matrix method where the inner region wavefunctions are obtained using a standard nuclear motion algorithm. Results are given for eigenphases and scattering lengths. Excellent agreement is obtained in all cases. Progress in developing a general procedure for treating ultra-low energy reactive and non-reactive collisions is discussed.Comment: 18 pages, 6 figures, 3 tables, conferenc